Controllability test for nonlinear datatic systems
Controllability is a fundamental property of control systems, serving as the prerequisite for controller design. While controllability test is well established in modelic (i.e., model-driven) control systems, extending it to datatic (i.e., data-driven) control systems is still a challenging task due...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Communications in Transportation Research |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S277242472400026X |
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| author | Yujie Yang Letian Tao Likun Wang Shengbo Eben Li |
| author_facet | Yujie Yang Letian Tao Likun Wang Shengbo Eben Li |
| author_sort | Yujie Yang |
| collection | DOAJ |
| description | Controllability is a fundamental property of control systems, serving as the prerequisite for controller design. While controllability test is well established in modelic (i.e., model-driven) control systems, extending it to datatic (i.e., data-driven) control systems is still a challenging task due to the absence of system models. In this study, we propose a general controllability test method for nonlinear systems with datatic description, where the system behaviors are merely described by data. In this situation, the state transition information of a dynamic system is available only at a limited number of data points, leaving the behaviors beyond these points unknown. Different from traditional exact controllability, we introduce a new concept called ϵ-controllability, which extends the definition from point-to-point form to point-to-region form. Accordingly, our focus shifts to checking whether the system state can be steered to a closed state ball centered on the target state, rather than exactly at that target state. Given a known state transition sample, the Lipschitz continuity assumption restricts the one-step transition of all the points in a state ball to a small neighborhood of the subsequent state. This property is referred to as one-step controllability backpropagation, i.e., if the states within this neighborhood are ϵ-controllable, those within the state ball are also ϵ-controllable. On its basis, we propose a tree search algorithm called maximum expansion of controllable subset (MECS) to identify controllable states in the dataset. Starting with a specific target state, our algorithm can iteratively propagate controllability from a known state ball to a new one. This iterative process gradually enlarges the ϵ-controllable subset by incorporating new controllable balls until all ϵ-controllable states are searched. Besides, a simplified version of MECS is proposed by solving a special shortest path problem, called Floyd expansion with radius fixed (FERF). FERF maintains a fixed radius of all controllable balls based on a mutual controllability assumption of neighboring states. The effectiveness of our method is validated in three datatic control systems whose dynamic behaviors are described by sampled data. |
| format | Article |
| id | doaj-art-dd9522ccf63e435f9063224e557da60b |
| institution | Kabale University |
| issn | 2772-4247 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Communications in Transportation Research |
| spelling | doaj-art-dd9522ccf63e435f9063224e557da60b2024-12-11T05:58:24ZengElsevierCommunications in Transportation Research2772-42472024-12-014100143Controllability test for nonlinear datatic systemsYujie Yang0Letian Tao1Likun Wang2Shengbo Eben Li3School of Vehicle and Mobility, Tsinghua University, Beijing, 100084, ChinaSchool of Vehicle and Mobility, Tsinghua University, Beijing, 100084, ChinaSchool of Vehicle and Mobility, Tsinghua University, Beijing, 100084, ChinaCorresponding author.; School of Vehicle and Mobility, Tsinghua University, Beijing, 100084, ChinaControllability is a fundamental property of control systems, serving as the prerequisite for controller design. While controllability test is well established in modelic (i.e., model-driven) control systems, extending it to datatic (i.e., data-driven) control systems is still a challenging task due to the absence of system models. In this study, we propose a general controllability test method for nonlinear systems with datatic description, where the system behaviors are merely described by data. In this situation, the state transition information of a dynamic system is available only at a limited number of data points, leaving the behaviors beyond these points unknown. Different from traditional exact controllability, we introduce a new concept called ϵ-controllability, which extends the definition from point-to-point form to point-to-region form. Accordingly, our focus shifts to checking whether the system state can be steered to a closed state ball centered on the target state, rather than exactly at that target state. Given a known state transition sample, the Lipschitz continuity assumption restricts the one-step transition of all the points in a state ball to a small neighborhood of the subsequent state. This property is referred to as one-step controllability backpropagation, i.e., if the states within this neighborhood are ϵ-controllable, those within the state ball are also ϵ-controllable. On its basis, we propose a tree search algorithm called maximum expansion of controllable subset (MECS) to identify controllable states in the dataset. Starting with a specific target state, our algorithm can iteratively propagate controllability from a known state ball to a new one. This iterative process gradually enlarges the ϵ-controllable subset by incorporating new controllable balls until all ϵ-controllable states are searched. Besides, a simplified version of MECS is proposed by solving a special shortest path problem, called Floyd expansion with radius fixed (FERF). FERF maintains a fixed radius of all controllable balls based on a mutual controllability assumption of neighboring states. The effectiveness of our method is validated in three datatic control systems whose dynamic behaviors are described by sampled data.http://www.sciencedirect.com/science/article/pii/S277242472400026XControllabilityDatatic systemsNonlinear systemsLipschitz continuity |
| spellingShingle | Yujie Yang Letian Tao Likun Wang Shengbo Eben Li Controllability test for nonlinear datatic systems Communications in Transportation Research Controllability Datatic systems Nonlinear systems Lipschitz continuity |
| title | Controllability test for nonlinear datatic systems |
| title_full | Controllability test for nonlinear datatic systems |
| title_fullStr | Controllability test for nonlinear datatic systems |
| title_full_unstemmed | Controllability test for nonlinear datatic systems |
| title_short | Controllability test for nonlinear datatic systems |
| title_sort | controllability test for nonlinear datatic systems |
| topic | Controllability Datatic systems Nonlinear systems Lipschitz continuity |
| url | http://www.sciencedirect.com/science/article/pii/S277242472400026X |
| work_keys_str_mv | AT yujieyang controllabilitytestfornonlineardataticsystems AT letiantao controllabilitytestfornonlineardataticsystems AT likunwang controllabilitytestfornonlineardataticsystems AT shengboebenli controllabilitytestfornonlineardataticsystems |